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1. Lyapunov Theory for 2-D Nonlinear Roesser Models: Application to Asymptotic and Exponential Stability.

Author

Yeganefar, Nima, Yeganefar, Nader, Ghamgui, Mariem, and Moulay, Emmanuel

Subjects
*EXPONENTIAL stability, *NONLINEAR statistical models, *LYAPUNOV functions, *ASYMPTOTIC controllability, *TRANSFER functions, *DISCRETE systems, *LINEAR systems, *TRAJECTORY optimization
Abstract

This technical note deals with a general class of discrete 2-D possibly nonlinear systems based on the Roesser model. We first motivate the introduction of Lyapunov type definitions of asymptotic and exponential stability. This will allow us to introduce and discuss several particularities that cannot be found in 1-D systems. Once this background has been carefully designed, we develop different Lyapunov theorems in order to check asymptotic and exponential stability of nonlinear 2-D systems. Finally we propose the first converse Lyapunov theorem in the case of exponential stability. [ABSTRACT FROM AUTHOR]

Published
2013
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